14:00 – 15:00 – Anna Calissano (Imperial College)

Title: Populations of Unlabeled Networks: Graph Space Geometry and Generalized Geodesic Regression Model

Abstract: Sets of graphs (or networks) arise in many different fields, from medicine to finance, from sport to the social sciences. The analysis of unlabeled graphs or networks is far from trivial due to the highly non-Euclidean nature of such data. We describe Graph Space as a possible geometric embedding for a set of unlabeled graphs, i.e. graphs with no node correspondence across observations. Graph Space is a quotient space, but it is not a manifold, requiring the definition of statistical methods beyond the tangent space approach. We introduce the Align All and Compute algorithm and use it for both estimating generalized geodesic principal components and generalized geodesic regression models, showing how to interpolate between unlabeled graphs. We demonstrate the flexibility of the framework on both simulated data, public transport system data and Fifa 2018 player passing network data.

Refreshments available between 15:00 – 15:30, Huxley Common Room (HXLY 549)